Montreal Geometric & Combinatorial Group Theory Seminar

Speaker: John Meier (Lafayette & Columbia)

Title: “Asymptotic cohomology
of the group of loops”

Date: 3:30PM, Monday, September 29, 2003

Place: Room 1120, Burnside Hall, McGill University

Abstract:

Let L_n denote n unknotted, unlinked circles in S^3. Much as
one can describe the n-strand braid group as the motion group of n points in a
disk, one can define the motion group of L_n in S^3: elements consist of finite
length movies where the n circles are allowed to fly about in the 3-sphere,
never intersecting, and returning to their original configuration at the end of
the film. This talk will focus on work with Jon McCammond, where we compute the
L^2 cohomology of this group. The argument eventually boils down to doing some
enumerative combinatorics on a poset of hypertrees.